What is the optimal transferprice at which the production

Question

Problem

The production division(p) of the Portland Electronics Company ("PEC") manufactures speakers that it sells internally to the marketing division (m), which promotes and distributes the speakers to the end customers. Assume that there is no external market for the speakers that are manufactured by the production division. The marketing division's market demand for the speakers in the end customer segment is:

P_m = 100 - 0.001Q_m

Where P_m is the selling price (in dollars per unit) and Q_m is the quantitysold (in units). The marketing division's total cost function(in dollars) is (excluding the price of speakers that it buys from the production division):

C_m = 300,000 + 10Q_m

The production division's total cost function (in dollars) is:

C_P = 500,000 + 15Q_P + 0.0005 Q_P²

Where Q_P is the total quantitysold and produced.

What is the optimal transferprice at which the production division sells the speakers to the marketing division so that the overall profits for PEC is maximized?